Further progress in hadron spectroscopy necessitates the phenomenological description of three particle reactions. We consider the isobar approximation, where the connected part of the 3 → 3 amplitude is first expressed as a sum over initial and final pairs, and then expanded into a truncated partial wave series. The resulting unitarity equation is automatically fulfilled by the B-matrix solution, which is an integral equation for the partial wave amplitudes, analogous to the K-matrix parameterization used to describe 2 → 2 amplitudes. We study the one particle exchange and how its analytic structure impacts rescattering solutions such as the triangle diagram. The analytic structure is compared to other parameterizations discussed in the literature. We briefly discuss the analogies with recent formalisms for extracting 3 → 3 scattering amplitudes in lattice QCD.

Mapping states with explicit gluonic degrees of freedom in the light sector is a challenge, and has led to controversies in the past. In particular, the experiments have reported two different hybrid candidates with spin-exotic signature, π1(1400) and π1 (1600), which couple separately to ηπ and η π. This picture is not compatible with recent Lattice QCD estimates for hybrid states, nor with most phenomenological models. We consider the recent partial wave analysis of the η ( ) π system by the COMPASS collaboration. We fit the extracted intensities and phases with a coupled-channel amplitude that enforces the unitarity and analyticity of the S-matrix. We provide a robust extraction of a single exotic π1 resonant pole, with mass and width 1564 ± 24 ± 86 MeV and 492 ± 54 ± 102 MeV, which couples to both η ( ) π channels. We find no evidence for a second exotic state. We also provide the resonance parameters of the a2(1320) and a 2 (1700).

In recent years, different on-shell 3 → 3 scattering formalisms have been proposed to be applied to both lattice QCD and infinite-volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in [M. T. Hansen and S. R. Sharpe, Phys. Rev. D 92, 114509 (2015).] and subsequently Briceño et al. in [R. A. Briceño, M. T. Hansen, and S. R. Sharpe, Phys. Rev. D 95, 074510 (2017).] can be recovered from the B-matrix representation, derived on the basis of S-matrix unitarity, presented by Mai et al. in [M. Mai, B. Hu, M. Döring, A. Pilloni, and A. Szczepaniak, Eur. Phys. J. A 53, 177 (2017).] and Jackura et al. in [A. Jackura, C. Fernández-Ramírez, V.

The reaction γN → ηN is studied in the high-energy regime (with photon lab energies E lab γ > 4 GeV) using information from the resonance region through the use of finite-energy sum rules (FESR). We illustrate how analyticity allows one to map the t-dependence of the unknown Regge residue functions. We provide predictions for the energy dependence of the beam asymmetry at high energies.

The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.